**Theorem.** The inclusion P --> G induces an isomorphism on
integral homology.

In the case p=0 (the vertex stabilizers), the group G is precisely SL_n(F[t]) and the group P is SL_n(F). In this case the theorem reduces to an unstable analogue of homotopy invariance in algebraic K-theory; namely, the integral homology of SL_n(F[t]) is the same as that of SL_n(F).

The theorem completes the computation of the E^1-term of the spectral sequence. The differential is difficult to calculate in general, but we are able to compute some special cases. In particular, we show that if F is an infinite field, then for n at least 3, the group H_2(SL_n(F[t,t^{-1}],Z) equals the direct sum of H_2(SL_n(F),Z) and the group of units of F.

This paper has been submitted for publication in the
*Annales Scientifiques de l'Ecole Normale Superieure.*

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Kevin P. Knudson <knudson@math.duke.edu>